Find `(dy)/(dx)=(1+x^(2))/(1+y^(2))`

The family of curves represented by (dy)/(dx)=(x^(2)+x+1)/(y^(2)+y+1) and the family represented by (dy)/(dx)+(y^(2)+y+1)/(x^(2)+x+1)=0

The solution of (dy)/(dx)=(x^2+y^2+1)/(2x y) satisfying y(1)=1 is given by

The solution of (dy)/(dx)=(x^2+y^2+1)/(2x y) satisfying y(1)=1 is given by

Find dy/dx if y=(x-1)^(1/2)

Find (dy)/(dx) ifcos(x-y)=1

Find (dy)/(dx) if 1+x^2+y^2=9

Find dy/dx if y= (x-1)/x^2

Find dy/dx if y(1-x^2)=6

Find (dy)/(dx)\ if (x^2+y^2)^2=x y

Find (dy)/(dx) if, tan^(-1)(x^2+y^2)=a